Objective
To determine the deformed state of a split circular ring under bending in its plane, without considering shear deformations.
Reference
Strength analyses in mechanical engineering / S.Ponomarev, V.Biderman, K.Likharev, etc. In three volumes. Volume 1. Moscow: Mashgiz, 1956.
Problem statement
To determine the deformed state of the ring.
Design model
A split circular ring is subjected to two mutually perpendicular loads Px and Py acting in the plane of the ring axis.
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Initial geometry of analytical model
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Initial geometry of FE model
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Geometry
Radius of the ring axis R = 1,3 m
Cross-sectional area F = 0,01 m2
Moment of inertia of the cross‑section I = 5 * 10-6 m4
Material properties
Modulus of elasticity Е = 2,0 * 1011 Pa
Loads
Concentrated load Px = Py = 1 kN
Note
Design model - plane model that consists of 120 bar elements of FE type 2 and 121 nodes.
Output data
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| Displacements u (mm) | Displacements v (mm) |
Comparison of calculation results
| Angle φ, rad | Displacement along X-axis | Displacement along Y-axis | ||||
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| Analytical solution | LIRA-FEM | Error, % | Analytical solution | LIRA-FEM | Error, % | |
| 0 | -6,902 | -6,9 | 0,03 | -20,706 | -20,7 | 0,03 |
| 45 | 2,69 | 2,86 | 6,32 | -16,777 | -16,6 | 1,06 |
| 90 | 6,275 | 6,26 | 0,24 | -8,472 | -8,88 | 4,82 |
| 135 | 3,984 | 3,95 | 0,85 | -2,419 | -2,39 | 1,20 |
| 180 | 0,943 | 0,941 | 0,21 | -0,943 | -0,943 | 0,00 |
| 225 | 0,154 | 0,158 | 2,60 | -1,125 | -1,126 | 1,91 |
| 270 | 0,316 | 0,315 | 0,32 | -0,627 | -0,639 | 0 |
| 315 | 0,114 | 0,12 | 5,26 | -0,074 | -0,081 | 9,46 |
| 360 | 0 | 0 | 0 | 0 | 0 | 0 |
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